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The magnetic origin of the outer boundaries of sunspots

This study demonstrates that the outer boundary of stable sunspots is defined by an invariant magnetic field strength of approximately 625G (the equipartition field), while the detachment of intensity and magnetic contours during decay reveals a distinct "super-equipartition" granular regime where convection persists despite elevated magnetic fields.

Original authors: Markus Schmassmann, Nazaret Bello González, Jan Jurčák, Rolf Schlichenmaier

Published 2026-02-20

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CC BY 4.0

Original authors: Markus Schmassmann, Nazaret Bello González, Jan Jurčák, Rolf Schlichenmaier

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Sun as a giant, churning pot of boiling soup. This "soup" is made of super-hot plasma, and it's constantly bubbling up in little cells called granules. These granules are like bubbles in a pot of boiling water, rising, popping, and mixing the heat around.

Now, imagine you drop a giant, heavy magnet into that pot. The magnet is so strong that it stops the soup from bubbling right around it. This creates a dark, calm island in the middle of the boiling chaos. This dark island is a sunspot.

For a long time, scientists have looked at sunspots and tried to figure out exactly where the "dark island" ends and the "boiling soup" begins. They usually just looked at how dark or bright the spot was (its intensity) to draw a line around it. But this paper asks a deeper question: Is that line just about brightness, or is there a hidden magnetic rulebook that actually draws the border?

The Discovery: The "Magnetic Fence"

The authors of this paper studied a very long-lived sunspot (like a stubborn storm that refuses to leave) as it traveled across the face of the Sun. They used a satellite (SDO) to take thousands of pictures, looking at two things simultaneously:

How bright the surface is (the boiling soup).
How strong the magnetic field is (the invisible magnet).

The Big Finding:
When the sunspot was healthy and stable, the line where the spot looked dark (the edge of the "island") matched perfectly with a specific magnetic strength: 625 Gauss.

Think of it like this: Imagine you are walking through a forest. You decide to stop walking exactly when the trees get so dense that you can't see the sky anymore. You might think you are stopping because of the light, but actually, you are stopping because the density of the trees hit a specific number.

In this case, the "trees" are magnetic field lines. The sunspot's outer edge isn't just a random dark line; it's a magnetic fence. As long as the magnetic field is stronger than 625 Gauss, the "boiling soup" (convection) is suppressed, and the spot stays dark. Once the field drops below that 625 Gauss "fence," the soup starts bubbling again, and the spot ends.

The "Super-Equipartition" Zone: A New Kind of Bubble

The most exciting part of the paper happens when the sunspot starts to die (decay).

Usually, when a sunspot dies, the dark center shrinks, and the "fence" (the 625 Gauss line) shrinks with it. But the authors found something weird. As the spot decayed, the dark edge (where the light returns) pulled back quickly, but the magnetic fence (the 625 Gauss line) stayed out further.

This created a strange gap between the dark spot and the magnetic fence.

Inside the gap: The magnetic field was still strong (stronger than the "fence" limit), but the spot was no longer dark.
What was happening there? The "boiling soup" (granules) was still bubbling, but the bubbles were smaller and brighter than normal.

The authors call this a "Super-Equipartition Granular Regime."

Here's an analogy:
Imagine a traffic cop (the magnetic field) standing in the middle of a busy street (the Sun's surface).

Normal Granules: The cop is weak; cars (bubbles) zoom past freely.
Sunspot Umbra: The cop is super strong; he stops all traffic. The street is empty and dark.
Sunspot Penumbra: The cop is strong enough to slow traffic down and make it flow in lanes, but not stop it completely.
The New Discovery (Super-Equipartition): The cop is still strong enough to stop the big trucks (normal bubbles), but he's too weak to stop the small motorcycles (tiny, bright bubbles). So, you see a lot of tiny, fast-moving motorcycles zipping around, even though the "big traffic" is still suppressed.

Why Does This Matter?

This paper changes how we understand the Sun's surface.

It's not about light; it's about physics: The edge of a sunspot isn't just a visual trick; it's a precise physical boundary defined by the balance between magnetic energy and the energy of the moving gas.
A new "weather" pattern: We now know there is a third type of "weather" on the Sun, distinct from the calm center (umbra) and the filamentary edge (penumbra). It's a zone where the magnetic field is strong enough to shrink the bubbles but not strong enough to kill them.

The Takeaway

The authors conclude that the outer boundary of a sunspot is drawn by an invisible, unchangeable rule: The Equipartition Field. It's the exact point where the Sun's magnetic power equals the power of its churning gas. When the sunspot is healthy, this magnetic fence perfectly matches the dark edge. When the sunspot dies, the fence stays put for a while, revealing a hidden world of tiny, bright bubbles that we didn't know existed before.

In short: Sunspots don't just have a "shadow"; they have a magnetic moat, and the water in that moat has a very specific depth that determines where the storm ends and the calm begins.

1. Problem Statement

While sunspots are the most prominent manifestation of solar magnetism, the physical nature of their outer boundaries (the edge of the penumbra) has remained poorly characterized. Previous attempts to define this boundary using geometric fits or radial magnetic profiles yielded inconclusive results. Although it is known that the inner boundary (umbra-penumbra) is defined by a specific magnetic threshold (the Jurčák criterion), the magnetic property defining the outer boundary of the penumbra has not been fully established. The authors aim to identify the specific magnetic property that delineates the transition from the sunspot penumbra to the surrounding photospheric granulation.

2. Methodology

The study utilizes high-resolution, time-series data from the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO).

Target: The long-lived Active Region NOAA 11591 (and its successor 11612), observed during two separate disc passages in 2012. The first passage represented a stable phase, while the second showed clear signs of decay.
Data Analysis:
- Contours: The authors compared two sets of contours:
  1. Intensity Contours: Defined by continuum intensity ( $I_c$ ) relative to the quiet Sun ( $I_{qs}$ ).
  2. Magnetic Contours: Defined by the absolute magnetic field strength ( $|B|$ ).
- Optimization: To account for the different formation heights of the continuum intensity and the Fe I 617.3 nm spectral line (used for magnetic inversion), a height difference ( $\Delta h$ ) was applied to the coordinates. The optimal $\Delta h$ and the intensity threshold were determined by minimizing the average distance ( $\langle d \rangle_{\psi,t}$ ) between the intensity and magnetic contours.
- Statistical Fitting: The magnetic field values along the intensity contours were fitted with sinusoidal functions to remove orbital artifacts (due to SDO's geosynchronous motion) and to determine a stable time-averaged magnetic offset ( $X_0$ ).

3. Key Results

A. Stable Phase (First Disc Passage)

Perfect Match: During the stable phase, the outer boundary of the sunspot (defined by an intensity contour of $0.9 I_{qs}$ ) aligns almost perfectly with the magnetic isocontour of 625 G.
Precision: The time-averaged mismatch between the two contours is minimized to 0.58 pixels (approx. 0.26 arcseconds).
Stability: The mean magnetic field strength along the boundary remains remarkably constant at 625 G over a period of more than 9 days, despite local fluctuations caused by convective cells.
Conclusion for Stable Spots: The outer boundary of a stable sunspot is defined by an invariant magnetic field strength, identified as the equipartition field ( $B_{eq}$ ).

B. Decay Phase (Second Disc Passage)

Detachment: As the sunspot decays and the penumbra disappears, the $0.9 I_{qs}$ intensity contour retracts inward toward the umbra. However, the 625 G magnetic isocontour remains further out.
Super-Equipartition Regime: The area between the retracted intensity boundary and the 625 G magnetic contour represents a "naked" region where the magnetic field is super-equipartition ( $|B| > B_{eq}$ ) but sub-critical (below the threshold required to suppress convection entirely).
Granulation: In this region, bright but smaller granules are observed. The magnetic field is strong enough to influence the granulation (reducing cell size) but not strong enough to suppress overturning convection or form a penumbra.

4. Key Contributions

Identification of the Equipartition Field: The paper provides observational evidence that the outer boundary of sunspots is physically defined by the equipartition field (where magnetic energy density equals kinetic energy density of the plasma flow).
Quantification: The study quantifies this boundary for SDO/HMI data at 625 G (at the continuum formation height), confirming theoretical predictions from MHD simulations (e.g., Jurčák et al. 2020).
Discovery of a New Convective Regime: The authors identify a "super-equipartition granular regime." This regime exists where the magnetic field exceeds the equipartition limit but remains below the critical value for convection suppression. In this regime, granulation persists but is modified (smaller, brighter cells) by the magnetic field.
Explanation of Penumbral Extent: The findings explain why penumbral extensions are consistently ~0.6 times the spot radius regardless of spot size. The penumbra extends outward until the magnetic field drops to the equipartition limit; larger spots with stronger fields simply have wider penumbras to reach this threshold.

5. Significance

Theoretical Validation: The results bridge the gap between theoretical magnetohydrostatic models (which predict a magnetopause at the equipartition field) and observational data.
Unified Framework: It unifies the understanding of sunspot boundaries:
- Inner Boundary: Defined by the Jurčák criterion (critical field for convection suppression).
- Outer Boundary: Defined by the equipartition field (balance between magnetic and kinetic energy).
Implications for Pores and Plage: The concept of the "super-equipartition granular regime" helps explain the morphology of pores and plage regions, where magnetic fields are strong enough to modify granulation but not strong enough to create a penumbra or umbra.
Future Diagnostics: The paper suggests that future inversion codes capable of retrieving reliable plasma densities and horizontal velocities will allow for the direct empirical calculation of the equipartition field ( $B_{eq} = \sqrt{4\pi\rho}v$ ), further validating this boundary definition.

In summary, Schmassmann et al. demonstrate that the visible edge of a sunspot is not an arbitrary intensity threshold but a fundamental magnetic boundary where the plasma flow and magnetic forces reach a state of equipartition.